Will online luundry and drycleaning service success in united kingdom?

I can't see anyone shipping clothes for cleaning, if that's what you mean.
It's a local business, and a Facebook page is a good way to advertise locally.

I'm not sure how you can clean laundry online. Soap and water don't travel through ethernet cables ;).

So what you must be talking about is a pickup and delivery service. If so, advertising online is one way of promoting your business. However since such a business is very local, there may be better ways.

In the USA, that is a very small profit margin business with high start up costs. And existing businesses have a strong advantage over anyone trying to come in. So strong you might not make ANY money for years before you turn a profit.

I will assume or guess you mean that someone will order the service online, and a local person would pick up the clothes, have them cleaned and then delivered.

This would be a luxury idea normally for richer people, but many places offer it, by phone call already.

Any idea could work, if you have the money to advertise, and to get the business going.